← MES Jr. Grade
Past Questions
If the number of arrival in a queue follows the Poisson distribution, then the inter arrival time obeys which one of the following distributions?
A)
Poisson’s distribution
B)
Negative exponential law
C)
Normal distribution
D)
Binomial
In Queueing Theory and Stochastic Processes, there is a fundamental mathematical relationship between the Poisson distribution and the Exponential distribution.
1. **Poisson Distribution**: This describes the number of events (arrivals) occurring within a fixed interval of time. If arrivals occur independently and at a constant average rate (λ), the probability of 'k' arrivals in time 't' is given by the Poisson formula.
2. **Inter-arrival Time**: This is the time elapsed between two successive arrivals.
3. **The Relationship**: If the number of arrivals follows a Poisson distribution with rate λ, the time between these arrivals follows an Exponential distribution (also known as the Negative Exponential law). Mathematically, the probability that the inter-arrival time 'T' is greater than a value 't' is equivalent to the probability that zero arrivals occur in the interval [0, t].
Using the Poisson formula: P(X=0) = (e^(-λt) * (λt)^0) / 0! = e^(-λt).
The Cumulative Distribution Function (CDF) of the inter-arrival time is therefore F(t) = 1 - e^(-λt), which is the CDF of the Exponential distribution.
**Why other options are incorrect:**
- **a. Poisson's distribution**: This describes the *count* of events, not the *time* between them. Time is a continuous variable, whereas Poisson is a discrete distribution.
- **c. Normal distribution**: This is a symmetric bell-shaped curve used for sums of independent variables (Central Limit Theorem), not for the memoryless inter-arrival times of a Poisson process.
- **d. Binomial**: This describes the number of successes in a fixed number of independent Bernoulli trials, which is not applicable to continuous time intervals.
Which of the following method is NOT used for obtaining the initial basic feasible solution in transportation problems?
A)
North west corner method
B)
Least cost entry method
C)
Vogel’s approximation method
D)
MODI method
In Transportation Problems (a specialized type of Linear Programming Problem), the solution process is divided into two main phases: finding an Initial Basic Feasible Solution (IBFS) and then testing that solution for optimality.
1. Initial Basic Feasible Solution (IBFS) methods are used to get a starting point. Common methods include:
- North West Corner Method (NWCM): A simple method that ignores costs and starts from the top-left cell.
- Least Cost Method (LCM): A method that prioritizes cells with the lowest unit transportation cost.
- Vogel's Approximation Method (VAM): A more sophisticated method using 'penalties' to find a solution closer to the optimum.
2. Optimality Testing methods are used to check if the IBFS can be improved to reduce the total cost. The most common methods for this are:
- MODI Method (Modified Distribution Method), also known as the u-v method.
- Stepping Stone Method.
Since the MODI method is used for optimality testing (improving an existing solution) and NOT for obtaining the initial basic feasible solution, it is the correct answer.
Write the characteristics of a grinding wheel. Also, write the factors that affect the performance of the grinding wheel.
Which one of the following defects is ‘Schottky defect’?
A)
Vacancy defect
B)
Compositional defect
C)
Interstitial defect
D)
Surface defect
A Schottky defect is a type of point defect in ionic crystals that occurs when a stoichiometric number of cations and anions are missing from their regular lattice sites, creating vacancies. Because it involves the absence of atoms/ions from the lattice, it is classified as a 'Vacancy defect'.
Detailed analysis of options:
- (a) Vacancy defect: Correct. Schottky defects are characterized by missing pairs of ions (vacancies) to maintain electrical neutrality.
- (b) Compositional defect: Incorrect. These refer to defects where the chemical composition varies (like non-stoichiometric defects), whereas a Schottky defect maintains the stoichiometry of the crystal.
- (c) Interstitial defect: Incorrect. An interstitial defect occurs when an atom occupies a site that is not a normal lattice point. A Frenkel defect is an example of an interstitial-vacancy pair, but a Schottky defect specifically involves only vacancies.
- (d) Surface defect: Incorrect. Surface defects are 2D imperfections (like grain boundaries or external surfaces), whereas Schottky defects are 0D point defects.
Discuss in detail the various mechanisms of tool wear, such as flank wear, crater wear, notch wear, and built-up edge.
How does the distribution of heat between the tool, chip, and workpiece affect machining performance?
In investment casting, the primary reason for preheating the ceramic mould before pouring is:
A)
To reduce thermal shock and prevent mould cracking
B)
To improve surface roughness of the casting
C)
To accelerate solidification
D)
To remove trapped gases in molten metal
In investment casting (also known as lost-wax casting), the ceramic shell is relatively brittle. When molten metal is poured into a cold ceramic mould, the extreme temperature difference between the liquid metal and the mould material creates high internal stresses due to rapid thermal expansion. This phenomenon is known as thermal shock, which can lead to the cracking or shattering of the ceramic mould, resulting in casting defects like fins or leakage. Preheating the mould reduces this temperature gradient, thereby minimizing thermal shock and ensuring the structural integrity of the mould.
Analysis of other options:
- Option (b) is incorrect because preheating generally improves surface finish by allowing the metal to flow more smoothly before freezing, but it is not the 'primary reason' for the preheating process itself.
- Option (c) is incorrect because preheating actually slows down the solidification rate (by reducing the cooling rate), which is often desired to prevent premature freezing in thin sections.
- Option (d) is incorrect because removing trapped gases is typically achieved through the permeability of the mould or vacuum assistance, not by preheating the mould shell.
The crystal structure of austenite is:
A)
body centered cubic
B)
face centered cubic
C)
hexagonal closed packed
D)
body centered tetragonal
In the study of the Iron-Carbon equilibrium diagram, iron exists in different allotropic forms depending on the temperature.
1. **Austenite (γ-iron)**: This is the stable phase of iron between 912°C and 1394°C. It possesses a **Face Centered Cubic (FCC)** crystal structure. Because of the FCC arrangement, austenite has larger interstitial sites, allowing it to dissolve more carbon compared to ferrite.
2. **Ferrite (α-iron)**: This is the stable phase at room temperature (up to 912°C) and possesses a **Body Centered Cubic (BCC)** structure. This corresponds to option (a).
3. **Delta Ferrite (δ-iron)**: This is the stable phase at very high temperatures (above 1394°C) and also possesses a **Body Centered Cubic (BCC)** structure.
4. **Martensite**: When austenite is quenched rapidly, it transforms into a non-equilibrium phase called Martensite, which has a **Body Centered Tetragonal (BCT)** structure. This corresponds to option (d).
5. **Hexagonal Closed Packed (HCP)**: While some metals exhibit HCP structures, the standard phases of pure iron/steel (Austenite, Ferrite) do not. This corresponds to option (c).
Therefore, the crystal structure of austenite is specifically Face Centered Cubic (FCC).
The M and E systems in metrology are related to measurements of:
A)
screw thread
B)
flatness
C)
angularity
D)
surface finish
In metrology, surface roughness (surface finish) is measured using different systems of standards. The 'M' system and 'E' system refer to the classification of surface roughness based on the 'cut-off' length (the sampling length used to filter out waviness from roughness).
1. The 'M' system (often associated with the ISO/metric standards) and the 'E' system (often associated with older European or specific industrial standards) define the parameters for evaluating surface texture.
2. Surface finish measurement involves analyzing the profile of a surface to determine the average roughness (Ra) or peak-to-valley height (Rz). The choice between different systems (like M or E) typically dictates the sampling length and the evaluation length used to ensure the measurement is representative of the surface texture.
Why other options are incorrect:
- a. Screw threads are measured using pitch gauges, thread micrometers, or three-wire methods.
- b. Flatness is measured using surface plates, optical flats, or dial indicators.
- c. Angularity is measured using sine bars, bevel protractors, or autocollimators.
The properties of material to resist penetration by another material is known as:
A)
Impact strength
B)
Hardness
C)
Fatigue
D)
Resilience
Step-by-step reasoning:
1. Definition of Hardness: In material science, hardness is defined as the resistance of a material to localized plastic deformation, such as indentation, scratching, or penetration by a harder object. Common tests for hardness include the Brinell, Rockwell, and Vickers tests, which all measure the depth or area of penetration by a standardized indenter.
2. Analysis of other options:
- Impact strength (a): This refers to the ability of a material to absorb energy and plastically deform before fracturing under a high-rate load (sudden impact). It is measured by tests like the Charpy or Izod tests.
- Fatigue (c): This is the tendency of a material to break or fail under repeated or cyclic loading, even if the stress is below the yield strength.
- Resilience (d): This is the capacity of a material to absorb energy when it is deformed elastically and then release that energy upon unloading.
3. Conclusion: Since the question specifically asks for the property to resist 'penetration', the correct term is Hardness.
In melting furnaces, the primary function of a refractory lining is to:
A)
Increase heat transfer
B)
Protect furnace structure and contain molten metal
C)
Accelerate melting
D)
Prevent chemical reactions
In melting furnaces, refractories are materials (such as alumina, silica, or magnesia) that can withstand extremely high temperatures without melting or decomposing. Their primary functions are: 1) Thermal Insulation: They protect the outer structural shell of the furnace (usually made of steel) from the intense heat of the molten metal, preventing the shell from melting or warping. 2) Containment: They provide a chemically stable and physically robust vessel to hold the molten metal.
Why other options are incorrect:
- Option (a): Refractories are designed to be insulators; they actually decrease heat transfer to the outside environment to maintain high internal temperatures.
- Option (c): Refractories do not accelerate the melting process; the heating element or fuel source does. In fact, excessive lining thickness can slow down heating due to insulation.
- Option (d): While refractories are chosen for their chemical compatibility with the metal, their primary 'function' is structural protection and containment rather than acting as a catalyst or inhibitor for chemical reactions.
Manganese bronze contains:
A)
5% Mn
B)
10% Mn
C)
0.12% Mn
D)
None of these
Manganese bronze is a high-strength alloy primarily based on copper and zinc, with the addition of manganese, aluminum, and iron. According to metallurgical standards (and as referenced in Britannica), high-tensile manganese bronze typically contains manganese in the range of 2% to 5%. Among the given options, 5% Mn falls within this standard composition range. Option 'b' (10%) is too high for standard manganese bronze, and option 'c' (0.12%) is far too low to provide the characteristic strength and corrosion resistance associated with this specific alloy. Therefore, option 'a' is the most accurate choice.
In cold working:
A)
strength, hardness and ductility increase
B)
strength and hardness increase, but ductility decreases
C)
strength, hardness and ductility decrease
D)
strength and hardness decrease, but ductility increases
Cold working (also known as strain hardening or work hardening) is the process of plastically deforming a metal below its recrystallization temperature. During this process, the dislocation density within the crystal lattice increases significantly. As these dislocations move and interact, they become entangled and impede each other's motion, making it more difficult for further deformation to occur. This results in an increase in the material's yield strength and hardness. However, because the capacity for further plastic deformation is reduced as the material becomes 'saturated' with dislocations, the ductility (the ability of the material to deform plastically before fracture) decreases. Therefore, strength and hardness increase while ductility decreases.
A cast product of a particular material has dimensions 75 mm x 125 mm x 20 mm. The total solidification time for the cast product is found to be 2.0 minutes as calculated using Chvorinov’s rule having the index, n = 2. If under the identical casting conditions, the cast product shape is changed to a cylinder having diameter = 50 mm and height = 50 mm, find the total solidification time in minutes.
Derive the coordination number and the atomic packing fraction of an FCC unit cell.
What is Cast Iron? Write its important characteristics and uses.
Plastic deformation is caused by:
A)
stored elastic energy
B)
dislocation motion
C)
low value of modulus
D)
complex elastic stress
Plastic deformation refers to the permanent, non-reversible deformation of a material that occurs when the applied stress exceeds the yield strength. In crystalline materials (like metals), this process occurs primarily through a mechanism called 'slip'. Slip is the process by which planes of atoms slide over one another. This sliding is not a simultaneous movement of an entire plane of atoms, but rather the movement of linear defects known as 'dislocations' through the crystal lattice. As dislocations move, they break and reform bonds, allowing the material to deform permanently without fracturing.
Why other options are incorrect:
- a. Stored elastic energy: This is associated with elastic deformation (temporary), where the material returns to its original shape once the load is removed.
- c. Low value of modulus: The modulus of elasticity (Young's modulus) describes the stiffness of a material in the elastic region; it does not cause plastic deformation.
- d. Complex elastic stress: Elastic stress, by definition, results in elastic (reversible) deformation, not plastic (permanent) deformation.
Extrusion force does not depend upon the:
A)
extrusion ratio
B)
type of extrusion process
C)
material of the die
D)
working temperature
Extrusion force is the force required to push a metal billet through a die to create a desired cross-section. It is governed by the formula: F = A₀ * σ_f * ln(R), where A₀ is the initial area, σ_f is the flow stress of the material, and R is the extrusion ratio.
1. Extrusion Ratio (a): The force is directly proportional to the natural log of the extrusion ratio (R = A₀/A_final). A higher ratio requires more force.
2. Type of Extrusion Process (b): Direct extrusion requires more force than indirect extrusion because in direct extrusion, there is additional friction between the billet and the container wall, whereas in indirect extrusion, there is no relative motion between the billet and the container.
3. Working Temperature (d): The flow stress (σ_f) of the metal is highly dependent on temperature. Increasing the temperature reduces the yield strength of the material, thereby reducing the required extrusion force.
4. Material of the Die (c): While the die material must be strong and wear-resistant enough to withstand the process, the *force required to deform the workpiece* depends on the workpiece's properties and the geometry of the process, not the chemical composition or material of the die itself (assuming the die does not deform).
Explain the different types of crystal imperfections.
Which sequence correctly outlines the basic steps of powder metallurgy?
A)
Sintering -> Compaction -> Blending -> Finishing
B)
Blending -> Compaction -> Sintering -> Secondary operations
C)
Compaction -> Sintering -> Blending -> Finishing
D)
Blending -> Sintering -> Compaction -> Finishing
Powder Metallurgy (PM) is a metal-forming process that follows a specific logical sequence to transform metal powders into a solid part. The standard steps are:
1. **Blending/Mixing**: The first step involves mixing the primary metal powder with alloying elements and lubricants (to reduce friction during pressing) to ensure a homogeneous distribution of materials.
2. **Compaction**: The blended powder is pressed in a die at high pressure to create a 'green compact'. This gives the part its initial shape and provides enough structural integrity for handling.
3. **Sintering**: The green compact is heated in a controlled atmosphere furnace to a temperature below the melting point of the main constituent. This causes the particles to bond through atomic diffusion, significantly increasing the strength and density of the part.
4. **Secondary Operations (Finishing)**: Depending on the requirements, the sintered part may undergo further processes such as machining, plating, heat treatment, or infiltration to achieve final dimensions or properties.
Comparing this to the options:
- Option (a) is incorrect because sintering cannot happen before compaction.
- Option (c) is incorrect because blending must occur before the powder is compacted.
- Option (d) is incorrect because sintering must follow compaction, not precede it.
Use of more acetylene with less volume of oxygen in an oxyacetylene torch produces a ___________ flame.
A)
Neutral
B)
Oxidizing
C)
Carburizing
D)
None of these
In oxy-acetylene welding, the type of flame produced depends on the ratio of oxygen to acetylene. There are three primary types of flames:
1. **Neutral Flame**: Produced when equal volumes of oxygen and acetylene are used. It is used for most general welding purposes.
2. **Oxidizing Flame**: Produced when there is an excess of oxygen (more oxygen than acetylene). This flame is hotter and is typically used for welding brass or bronze.
3. **Carburizing Flame**: Produced when there is an excess of acetylene (more acetylene than oxygen). This flame contains unburnt carbon (acetylene), which creates a 'reducing' atmosphere. It is characterized by three distinct zones (inner cone, acetylene feather, and outer envelope) and is used for welding high-carbon steels, hard-facing, or aluminum.
Since the question specifies the use of 'more acetylene with less volume of oxygen', the resulting flame is a carburizing flame.
An organization uses ABC approach for categorization of its stock. Which of the following describe class C items?
A)
High value and high risk
B)
High value and low risk
C)
Low value and high risk
D)
Low value and low risk
The ABC analysis (Always Better Control) is an inventory categorization technique based on the Pareto Principle (the 80/20 rule). It classifies items based on their consumption value (Quantity × Unit Cost).
1. **Class A items**: These are the most valuable items. They typically represent about 10-20% of the total inventory items but account for 70-80% of the total consumption value. Because of their high value, they require strict control, frequent review, and carry a high risk if mismanaged.
2. **Class B items**: These are intermediate items. They typically represent about 30% of the inventory items and account for 15-20% of the total consumption value. They require moderate control.
3. **Class C items**: These are the least valuable items. They typically represent the majority of the inventory items (about 50%) but account for only a small fraction (about 5-10%) of the total consumption value. Because they are low in value, they are managed with loose control, bulk ordering, and are considered low risk in terms of financial impact if stock levels fluctuate slightly.
Therefore, Class C items are characterized as low value and low risk.
In shell moulding, the resin-coated sand is hardened by:
A)
Cooling
B)
Chemical catalyst
C)
Heating to cure the resin
D)
Applying pressure
Shell moulding is a precision casting process that uses a mixture of sand and a thermosetting resin binder. The process works as follows: 1. A metal pattern is heated to a specific temperature (typically 200-300°C). 2. Resin-coated sand is dropped onto the heated pattern. 3. The heat from the pattern causes the thermosetting resin to melt and then cure (polymerize), forming a hard, thin 'shell' around the pattern. 4. Once the shell is hardened, the excess uncured sand is dumped, and the shell is removed from the pattern.
Why other options are incorrect:
- a. Cooling: Cooling would not trigger the polymerization of a thermosetting resin; heat is required for the chemical reaction.
- b. Chemical catalyst: While some resins use catalysts, shell moulding specifically relies on thermal energy (heat) from the pattern to initiate curing.
- d. Applying pressure: Pressure is not the mechanism used to harden the resin in this process; the chemical bond is formed via thermal curing.
What is the iron-carbon diagram? Draw a neat and labelled schematic iron-carbon diagram (need not be in scale).
Stroke of ram of shaper is adjusted by:
A)
Changing the pinion
B)
Changing the position of the crank pin
C)
Changing the position of lead screw
D)
None of above
In a shaper machine, the reciprocating motion of the ram is typically driven by a crank and slotted link mechanism (a type of quick-return mechanism). The length of the stroke of the ram is directly proportional to the distance between the center of rotation of the crank and the crank pin. By moving the crank pin closer to the center of rotation, the throw of the crank decreases, thereby shortening the stroke of the ram. Conversely, moving the crank pin further from the center increases the stroke length.
Analysis of other options:
- Option (a): Changing the pinion would typically alter the speed of the machine or the feed rate, not the stroke length.
- Option (c): The lead screw is used for the automatic cross-feed of the table, not for controlling the longitudinal stroke of the ram.
- Option (d): Incorrect, as option (b) is the standard mechanical method for adjusting stroke length in shapers.